Two cards are drawn from a deck. Determine P(red or heart), P(jack or heart), P(red or ten) and P(red queen or black jack).

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The number of ways of choosing 2 cards from a deck is not 1326 but 52*51 = 2652

In terms of the formula P(A or B) = P(A) + P(B) - P(A and B).

P(red or heart) = P(red) + P(heart) - P(red and heart)

=> 26*25/52*52 + 13*12/52*51 -...

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The number of ways of choosing 2 cards from a deck is not 1326 but 52*51 = 2652

In terms of the formula P(A or B) = P(A) + P(B) - P(A and B).

P(red or heart) = P(red) + P(heart) - P(red and heart)

=> 26*25/52*52 + 13*12/52*51 - 13*12/52*51 = 26*25/52*51 = 25/102

P(jack or heart) = P(jack) + P(heart) - P(jack and heart) = 4*3/52*51 + 13*12/52*51 - 1*0/52*51 = 14/221

P(red or ten) = P(red) + P(ten) - P(red and ten) = 26*25/52*51 + 4*3/52*51 - 2*1/52*51 =  55/221

P(red queen or black jack) = P(red queen) + P(black jack) - P(red queen and black jack) = 2*1/52*51 + 2*1/52*51 - 0 = 1/663

P(red or heart) = 25/102, P(jack or heart) = 14/221, P(red or ten) = 55/221 and P(red queen or black jack) = 1/663

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